Robust control system calculations

[Naibos77]

can i solve this problem i didnt go university due to Covid-19

 

[anorlunda]

Welcome to PF.

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[Naibos77]

okey for problem 1 i wrote this MATLAB code :

clear all;
clc;
% Defining TF
s=tf('s');
G=4/((s-1)*(0.02*s+1)^2);
Gd=100/(10*s+1);

% Weight Selection
M=1.8; wb=20; A=1e-4;
Wp=tf([1/M wb], [1 wb*A]);
Wu=1;

% Hinf Controller Design
[K,CL,gamma]=mixsyn(G,Wp,Wu,[]);

[K_num, K_den] = ss2tf(K.a,K.b,K.c,K.d);

Ks = tf(K_num, K_den);

% Analysis
Gcl = minreal(feedback(G*Ks,1));

figure(1)
step(Gcl)
grid on

L = G*Ks;
S = minreal(1 / (1 + L));
KS = Ks*S;

figure(2)
bodemag(S,'b',KS,'g',gamma/Wp,'b--',ss(gamma/Wu),'g--')
legend('S','KS','gamma/Wp','gamma/Wu','Location','SE')
grid on

%figure(2)
%sigma(S,'b',KS,'g',gamma/Ws,'b--',ss(gamma/Wu),'g--')
%legend('S','KS','gamma/Ws','gamma/Wu','Location','SE')
%grid on

% Second Controller Weights
M2=1.5; wb2=10; A2=1e-4; n = 2;
Wp2 = (s/M2^(1/n) + wb2)^n / (s + wb2*A2^(1/n))^n;
Wu2=1;

% Second Hinf Controller Design
[K2,CL2,gamma2]=mixsyn(G,Wp2,Wu,[]);

[K2_num, K2_den] = ss2tf(K2.a,K2.b,K2.c,K2.d);

K2s = tf(K2_num, K2_den);

% Analysis
G2cl = minreal(feedback(G*K2s,1));

figure(3)
step(Gcl, G2cl)
legend('Design 1', 'Design 2')
grid on

L2 = G*K2s;
S2 = minreal(1 / (1 + L2));
KS2 = K2s*S2;

figure(4)
bodemag(S2,'b',KS2,'g',gamma2/Wp2,'b--',ss(gamma2/Wu2),'g--')
legend('S2','KS2','gamma2/Wp2','gamma2/Wu2','Location','SE')
grid on

figure(5)
bodemag(S,'b',S2,'m',gamma/Wp,'b--',gamma2/Wp2,'m--')
legend('S','S2','gamma/Wp','gamma2/Wp2','Location','SE')
grid on

figure(6)
step(S*Gd, S2*Gd, 2)
legend('Design 1', 'Design 2')
grid on

 

[Naibos77]

for question 2 :
clear all
clcDelta_I = ultidyn('Delta_I', [1 1]);
Delta_I = ultidyn('Delta_I', [1 1]);

G = tf(1,[0.1 1])

G1 = G*tf(1,[.05 1])

G2 = G*tf([-.01 1],[.01 1])

G3 = G*tf(4,[1 2 4])

G4 = G*tf(100,[1 2 100])
array = stack(1,G1,G2,G3,G4);
Garray = frd(array,logspace(-1,3,60));

rel_err = (Garray - G) / G;
figure(1)
bodemag(rel_err)
grid on

% Fitting multiplicative uncertainty weight
[Gp,Info] = ucover(Garray,G,1);

figure(2)
bodemag(rel_err,'b--',Info.W1,'r',{0.1,1000})
grid on

% Multiplicative Uncertainty Weight in tf form
[num_wI den_wI] = ss2tf(Info.W1.a,Info.W1.b,Info.W1.c,Info.W1.d);
wIs = tf(num_wI, den_wI);

% Other representation of Gp
Gp2 = G * (1 + wIs * Delta_I)